Edmund had fallen at the first hurdle in Melbourne on both of his two previous attempts but the 22-year-old outclassed Giraldo to win 6-2 7-5 6-3.
He joins compatriots Andy Murray and Dan Evans in round two and will meet Pablo Carreno Busta, the Spanish 30th seed and beneficiary of a fifth-set retirement from Canadian Peter Polansky.
Busta beat Edmund comfortably when they met at a Futures event in Spain three years ago but the Briton has improved immeasurably since then and will carry a genuine threat of an upset.
This time 12 months ago, Edmund had wilted in the heat here, crippled by cramp in a five-set defeat to little-known Bosnian Damir Dzumhur.
Another bout of pre-season in Miami with Murray appears to have done the trick, however, with the Yorkshireman experiencing no such problems this time in searing temperatures reaching around 36 degrees Celsius at Melbourne Park.
Although neither player appeared keen to shorten the rallies on Court Five, with only seven of the contest’s 163 points won at the net.
It was a baseline battle and Edmund was the winner, too consistent for Giraldo to keep up and his rasping forehand too heavy for the Colombian to match.
He stormed into an early 3-0 lead and despite an exchange of breaks at the end of the set, broke a third time to move one set clear.
Giraldo cranked up the pressure at 3-3 in the second as he led 0-30 on Edmund’s serve, but two forehands helped the Briton to hold.
He never looked back, breaking decisively himself at 6-5 when Giraldo shanked a backhand wide, and when his opponent mangled at his racket at the start of the final set, the game appeared to be up.
Edmund broke again, for the fifth time in the match at 4-3, before serving out to love, confirming his victory with an ace after an hour and 50 minutes.